### 63rd Putnam 2002

**Problem A2**

Given any 5 distinct points on the surface of a sphere, show that we can find a closed hemisphere which contains at least 4 of them.

**Solution**

Pigeonhole principle.

Take a great circle through two of the points. Then at least two of the other three points must lie in one of the hemispheres bounded by the great circle.

63rd Putnam 2002

© John Scholes

jscholes@kalva.demon.co.uk

11 Dec 2002